Polytope of Type {116,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {116,8}*1856b
if this polytope has a name.
Group : SmallGroup(1856,718)
Rank : 3
Schlafli Type : {116,8}
Number of vertices, edges, etc : 116, 464, 8
Order of s0s1s2 : 232
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {116,4}*928
4-fold quotients : {116,2}*464, {58,4}*464
8-fold quotients : {58,2}*232
16-fold quotients : {29,2}*116
29-fold quotients : {4,8}*64b
58-fold quotients : {4,4}*32
116-fold quotients : {2,4}*16, {4,2}*16
232-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,233)( 2,261)( 3,260)( 4,259)( 5,258)( 6,257)( 7,256)( 8,255)
( 9,254)( 10,253)( 11,252)( 12,251)( 13,250)( 14,249)( 15,248)( 16,247)
( 17,246)( 18,245)( 19,244)( 20,243)( 21,242)( 22,241)( 23,240)( 24,239)
( 25,238)( 26,237)( 27,236)( 28,235)( 29,234)( 30,262)( 31,290)( 32,289)
( 33,288)( 34,287)( 35,286)( 36,285)( 37,284)( 38,283)( 39,282)( 40,281)
( 41,280)( 42,279)( 43,278)( 44,277)( 45,276)( 46,275)( 47,274)( 48,273)
( 49,272)( 50,271)( 51,270)( 52,269)( 53,268)( 54,267)( 55,266)( 56,265)
( 57,264)( 58,263)( 59,291)( 60,319)( 61,318)( 62,317)( 63,316)( 64,315)
( 65,314)( 66,313)( 67,312)( 68,311)( 69,310)( 70,309)( 71,308)( 72,307)
( 73,306)( 74,305)( 75,304)( 76,303)( 77,302)( 78,301)( 79,300)( 80,299)
( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)( 88,320)
( 89,348)( 90,347)( 91,346)( 92,345)( 93,344)( 94,343)( 95,342)( 96,341)
( 97,340)( 98,339)( 99,338)(100,337)(101,336)(102,335)(103,334)(104,333)
(105,332)(106,331)(107,330)(108,329)(109,328)(110,327)(111,326)(112,325)
(113,324)(114,323)(115,322)(116,321)(117,378)(118,406)(119,405)(120,404)
(121,403)(122,402)(123,401)(124,400)(125,399)(126,398)(127,397)(128,396)
(129,395)(130,394)(131,393)(132,392)(133,391)(134,390)(135,389)(136,388)
(137,387)(138,386)(139,385)(140,384)(141,383)(142,382)(143,381)(144,380)
(145,379)(146,349)(147,377)(148,376)(149,375)(150,374)(151,373)(152,372)
(153,371)(154,370)(155,369)(156,368)(157,367)(158,366)(159,365)(160,364)
(161,363)(162,362)(163,361)(164,360)(165,359)(166,358)(167,357)(168,356)
(169,355)(170,354)(171,353)(172,352)(173,351)(174,350)(175,436)(176,464)
(177,463)(178,462)(179,461)(180,460)(181,459)(182,458)(183,457)(184,456)
(185,455)(186,454)(187,453)(188,452)(189,451)(190,450)(191,449)(192,448)
(193,447)(194,446)(195,445)(196,444)(197,443)(198,442)(199,441)(200,440)
(201,439)(202,438)(203,437)(204,407)(205,435)(206,434)(207,433)(208,432)
(209,431)(210,430)(211,429)(212,428)(213,427)(214,426)(215,425)(216,424)
(217,423)(218,422)(219,421)(220,420)(221,419)(222,418)(223,417)(224,416)
(225,415)(226,414)(227,413)(228,412)(229,411)(230,410)(231,409)(232,408)
(465,697)(466,725)(467,724)(468,723)(469,722)(470,721)(471,720)(472,719)
(473,718)(474,717)(475,716)(476,715)(477,714)(478,713)(479,712)(480,711)
(481,710)(482,709)(483,708)(484,707)(485,706)(486,705)(487,704)(488,703)
(489,702)(490,701)(491,700)(492,699)(493,698)(494,726)(495,754)(496,753)
(497,752)(498,751)(499,750)(500,749)(501,748)(502,747)(503,746)(504,745)
(505,744)(506,743)(507,742)(508,741)(509,740)(510,739)(511,738)(512,737)
(513,736)(514,735)(515,734)(516,733)(517,732)(518,731)(519,730)(520,729)
(521,728)(522,727)(523,755)(524,783)(525,782)(526,781)(527,780)(528,779)
(529,778)(530,777)(531,776)(532,775)(533,774)(534,773)(535,772)(536,771)
(537,770)(538,769)(539,768)(540,767)(541,766)(542,765)(543,764)(544,763)
(545,762)(546,761)(547,760)(548,759)(549,758)(550,757)(551,756)(552,784)
(553,812)(554,811)(555,810)(556,809)(557,808)(558,807)(559,806)(560,805)
(561,804)(562,803)(563,802)(564,801)(565,800)(566,799)(567,798)(568,797)
(569,796)(570,795)(571,794)(572,793)(573,792)(574,791)(575,790)(576,789)
(577,788)(578,787)(579,786)(580,785)(581,842)(582,870)(583,869)(584,868)
(585,867)(586,866)(587,865)(588,864)(589,863)(590,862)(591,861)(592,860)
(593,859)(594,858)(595,857)(596,856)(597,855)(598,854)(599,853)(600,852)
(601,851)(602,850)(603,849)(604,848)(605,847)(606,846)(607,845)(608,844)
(609,843)(610,813)(611,841)(612,840)(613,839)(614,838)(615,837)(616,836)
(617,835)(618,834)(619,833)(620,832)(621,831)(622,830)(623,829)(624,828)
(625,827)(626,826)(627,825)(628,824)(629,823)(630,822)(631,821)(632,820)
(633,819)(634,818)(635,817)(636,816)(637,815)(638,814)(639,900)(640,928)
(641,927)(642,926)(643,925)(644,924)(645,923)(646,922)(647,921)(648,920)
(649,919)(650,918)(651,917)(652,916)(653,915)(654,914)(655,913)(656,912)
(657,911)(658,910)(659,909)(660,908)(661,907)(662,906)(663,905)(664,904)
(665,903)(666,902)(667,901)(668,871)(669,899)(670,898)(671,897)(672,896)
(673,895)(674,894)(675,893)(676,892)(677,891)(678,890)(679,889)(680,888)
(681,887)(682,886)(683,885)(684,884)(685,883)(686,882)(687,881)(688,880)
(689,879)(690,878)(691,877)(692,876)(693,875)(694,874)(695,873)(696,872);;
s1 := ( 1, 2)( 3, 29)( 4, 28)( 5, 27)( 6, 26)( 7, 25)( 8, 24)( 9, 23)
( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)( 32, 58)
( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)( 40, 50)
( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)( 63, 85)
( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)
( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)
( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)(102,104)
(117,147)(118,146)(119,174)(120,173)(121,172)(122,171)(123,170)(124,169)
(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)
(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,154)(140,153)
(141,152)(142,151)(143,150)(144,149)(145,148)(175,205)(176,204)(177,232)
(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)(185,224)
(186,223)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)(193,216)
(194,215)(195,214)(196,213)(197,212)(198,211)(199,210)(200,209)(201,208)
(202,207)(203,206)(233,292)(234,291)(235,319)(236,318)(237,317)(238,316)
(239,315)(240,314)(241,313)(242,312)(243,311)(244,310)(245,309)(246,308)
(247,307)(248,306)(249,305)(250,304)(251,303)(252,302)(253,301)(254,300)
(255,299)(256,298)(257,297)(258,296)(259,295)(260,294)(261,293)(262,321)
(263,320)(264,348)(265,347)(266,346)(267,345)(268,344)(269,343)(270,342)
(271,341)(272,340)(273,339)(274,338)(275,337)(276,336)(277,335)(278,334)
(279,333)(280,332)(281,331)(282,330)(283,329)(284,328)(285,327)(286,326)
(287,325)(288,324)(289,323)(290,322)(349,437)(350,436)(351,464)(352,463)
(353,462)(354,461)(355,460)(356,459)(357,458)(358,457)(359,456)(360,455)
(361,454)(362,453)(363,452)(364,451)(365,450)(366,449)(367,448)(368,447)
(369,446)(370,445)(371,444)(372,443)(373,442)(374,441)(375,440)(376,439)
(377,438)(378,408)(379,407)(380,435)(381,434)(382,433)(383,432)(384,431)
(385,430)(386,429)(387,428)(388,427)(389,426)(390,425)(391,424)(392,423)
(393,422)(394,421)(395,420)(396,419)(397,418)(398,417)(399,416)(400,415)
(401,414)(402,413)(403,412)(404,411)(405,410)(406,409)(465,582)(466,581)
(467,609)(468,608)(469,607)(470,606)(471,605)(472,604)(473,603)(474,602)
(475,601)(476,600)(477,599)(478,598)(479,597)(480,596)(481,595)(482,594)
(483,593)(484,592)(485,591)(486,590)(487,589)(488,588)(489,587)(490,586)
(491,585)(492,584)(493,583)(494,611)(495,610)(496,638)(497,637)(498,636)
(499,635)(500,634)(501,633)(502,632)(503,631)(504,630)(505,629)(506,628)
(507,627)(508,626)(509,625)(510,624)(511,623)(512,622)(513,621)(514,620)
(515,619)(516,618)(517,617)(518,616)(519,615)(520,614)(521,613)(522,612)
(523,640)(524,639)(525,667)(526,666)(527,665)(528,664)(529,663)(530,662)
(531,661)(532,660)(533,659)(534,658)(535,657)(536,656)(537,655)(538,654)
(539,653)(540,652)(541,651)(542,650)(543,649)(544,648)(545,647)(546,646)
(547,645)(548,644)(549,643)(550,642)(551,641)(552,669)(553,668)(554,696)
(555,695)(556,694)(557,693)(558,692)(559,691)(560,690)(561,689)(562,688)
(563,687)(564,686)(565,685)(566,684)(567,683)(568,682)(569,681)(570,680)
(571,679)(572,678)(573,677)(574,676)(575,675)(576,674)(577,673)(578,672)
(579,671)(580,670)(697,901)(698,900)(699,928)(700,927)(701,926)(702,925)
(703,924)(704,923)(705,922)(706,921)(707,920)(708,919)(709,918)(710,917)
(711,916)(712,915)(713,914)(714,913)(715,912)(716,911)(717,910)(718,909)
(719,908)(720,907)(721,906)(722,905)(723,904)(724,903)(725,902)(726,872)
(727,871)(728,899)(729,898)(730,897)(731,896)(732,895)(733,894)(734,893)
(735,892)(736,891)(737,890)(738,889)(739,888)(740,887)(741,886)(742,885)
(743,884)(744,883)(745,882)(746,881)(747,880)(748,879)(749,878)(750,877)
(751,876)(752,875)(753,874)(754,873)(755,843)(756,842)(757,870)(758,869)
(759,868)(760,867)(761,866)(762,865)(763,864)(764,863)(765,862)(766,861)
(767,860)(768,859)(769,858)(770,857)(771,856)(772,855)(773,854)(774,853)
(775,852)(776,851)(777,850)(778,849)(779,848)(780,847)(781,846)(782,845)
(783,844)(784,814)(785,813)(786,841)(787,840)(788,839)(789,838)(790,837)
(791,836)(792,835)(793,834)(794,833)(795,832)(796,831)(797,830)(798,829)
(799,828)(800,827)(801,826)(802,825)(803,824)(804,823)(805,822)(806,821)
(807,820)(808,819)(809,818)(810,817)(811,816)(812,815);;
s2 := ( 1,465)( 2,466)( 3,467)( 4,468)( 5,469)( 6,470)( 7,471)( 8,472)
( 9,473)( 10,474)( 11,475)( 12,476)( 13,477)( 14,478)( 15,479)( 16,480)
( 17,481)( 18,482)( 19,483)( 20,484)( 21,485)( 22,486)( 23,487)( 24,488)
( 25,489)( 26,490)( 27,491)( 28,492)( 29,493)( 30,494)( 31,495)( 32,496)
( 33,497)( 34,498)( 35,499)( 36,500)( 37,501)( 38,502)( 39,503)( 40,504)
( 41,505)( 42,506)( 43,507)( 44,508)( 45,509)( 46,510)( 47,511)( 48,512)
( 49,513)( 50,514)( 51,515)( 52,516)( 53,517)( 54,518)( 55,519)( 56,520)
( 57,521)( 58,522)( 59,552)( 60,553)( 61,554)( 62,555)( 63,556)( 64,557)
( 65,558)( 66,559)( 67,560)( 68,561)( 69,562)( 70,563)( 71,564)( 72,565)
( 73,566)( 74,567)( 75,568)( 76,569)( 77,570)( 78,571)( 79,572)( 80,573)
( 81,574)( 82,575)( 83,576)( 84,577)( 85,578)( 86,579)( 87,580)( 88,523)
( 89,524)( 90,525)( 91,526)( 92,527)( 93,528)( 94,529)( 95,530)( 96,531)
( 97,532)( 98,533)( 99,534)(100,535)(101,536)(102,537)(103,538)(104,539)
(105,540)(106,541)(107,542)(108,543)(109,544)(110,545)(111,546)(112,547)
(113,548)(114,549)(115,550)(116,551)(117,610)(118,611)(119,612)(120,613)
(121,614)(122,615)(123,616)(124,617)(125,618)(126,619)(127,620)(128,621)
(129,622)(130,623)(131,624)(132,625)(133,626)(134,627)(135,628)(136,629)
(137,630)(138,631)(139,632)(140,633)(141,634)(142,635)(143,636)(144,637)
(145,638)(146,581)(147,582)(148,583)(149,584)(150,585)(151,586)(152,587)
(153,588)(154,589)(155,590)(156,591)(157,592)(158,593)(159,594)(160,595)
(161,596)(162,597)(163,598)(164,599)(165,600)(166,601)(167,602)(168,603)
(169,604)(170,605)(171,606)(172,607)(173,608)(174,609)(175,639)(176,640)
(177,641)(178,642)(179,643)(180,644)(181,645)(182,646)(183,647)(184,648)
(185,649)(186,650)(187,651)(188,652)(189,653)(190,654)(191,655)(192,656)
(193,657)(194,658)(195,659)(196,660)(197,661)(198,662)(199,663)(200,664)
(201,665)(202,666)(203,667)(204,668)(205,669)(206,670)(207,671)(208,672)
(209,673)(210,674)(211,675)(212,676)(213,677)(214,678)(215,679)(216,680)
(217,681)(218,682)(219,683)(220,684)(221,685)(222,686)(223,687)(224,688)
(225,689)(226,690)(227,691)(228,692)(229,693)(230,694)(231,695)(232,696)
(233,697)(234,698)(235,699)(236,700)(237,701)(238,702)(239,703)(240,704)
(241,705)(242,706)(243,707)(244,708)(245,709)(246,710)(247,711)(248,712)
(249,713)(250,714)(251,715)(252,716)(253,717)(254,718)(255,719)(256,720)
(257,721)(258,722)(259,723)(260,724)(261,725)(262,726)(263,727)(264,728)
(265,729)(266,730)(267,731)(268,732)(269,733)(270,734)(271,735)(272,736)
(273,737)(274,738)(275,739)(276,740)(277,741)(278,742)(279,743)(280,744)
(281,745)(282,746)(283,747)(284,748)(285,749)(286,750)(287,751)(288,752)
(289,753)(290,754)(291,784)(292,785)(293,786)(294,787)(295,788)(296,789)
(297,790)(298,791)(299,792)(300,793)(301,794)(302,795)(303,796)(304,797)
(305,798)(306,799)(307,800)(308,801)(309,802)(310,803)(311,804)(312,805)
(313,806)(314,807)(315,808)(316,809)(317,810)(318,811)(319,812)(320,755)
(321,756)(322,757)(323,758)(324,759)(325,760)(326,761)(327,762)(328,763)
(329,764)(330,765)(331,766)(332,767)(333,768)(334,769)(335,770)(336,771)
(337,772)(338,773)(339,774)(340,775)(341,776)(342,777)(343,778)(344,779)
(345,780)(346,781)(347,782)(348,783)(349,842)(350,843)(351,844)(352,845)
(353,846)(354,847)(355,848)(356,849)(357,850)(358,851)(359,852)(360,853)
(361,854)(362,855)(363,856)(364,857)(365,858)(366,859)(367,860)(368,861)
(369,862)(370,863)(371,864)(372,865)(373,866)(374,867)(375,868)(376,869)
(377,870)(378,813)(379,814)(380,815)(381,816)(382,817)(383,818)(384,819)
(385,820)(386,821)(387,822)(388,823)(389,824)(390,825)(391,826)(392,827)
(393,828)(394,829)(395,830)(396,831)(397,832)(398,833)(399,834)(400,835)
(401,836)(402,837)(403,838)(404,839)(405,840)(406,841)(407,871)(408,872)
(409,873)(410,874)(411,875)(412,876)(413,877)(414,878)(415,879)(416,880)
(417,881)(418,882)(419,883)(420,884)(421,885)(422,886)(423,887)(424,888)
(425,889)(426,890)(427,891)(428,892)(429,893)(430,894)(431,895)(432,896)
(433,897)(434,898)(435,899)(436,900)(437,901)(438,902)(439,903)(440,904)
(441,905)(442,906)(443,907)(444,908)(445,909)(446,910)(447,911)(448,912)
(449,913)(450,914)(451,915)(452,916)(453,917)(454,918)(455,919)(456,920)
(457,921)(458,922)(459,923)(460,924)(461,925)(462,926)(463,927)(464,928);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(928)!( 1,233)( 2,261)( 3,260)( 4,259)( 5,258)( 6,257)( 7,256)
( 8,255)( 9,254)( 10,253)( 11,252)( 12,251)( 13,250)( 14,249)( 15,248)
( 16,247)( 17,246)( 18,245)( 19,244)( 20,243)( 21,242)( 22,241)( 23,240)
( 24,239)( 25,238)( 26,237)( 27,236)( 28,235)( 29,234)( 30,262)( 31,290)
( 32,289)( 33,288)( 34,287)( 35,286)( 36,285)( 37,284)( 38,283)( 39,282)
( 40,281)( 41,280)( 42,279)( 43,278)( 44,277)( 45,276)( 46,275)( 47,274)
( 48,273)( 49,272)( 50,271)( 51,270)( 52,269)( 53,268)( 54,267)( 55,266)
( 56,265)( 57,264)( 58,263)( 59,291)( 60,319)( 61,318)( 62,317)( 63,316)
( 64,315)( 65,314)( 66,313)( 67,312)( 68,311)( 69,310)( 70,309)( 71,308)
( 72,307)( 73,306)( 74,305)( 75,304)( 76,303)( 77,302)( 78,301)( 79,300)
( 80,299)( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)
( 88,320)( 89,348)( 90,347)( 91,346)( 92,345)( 93,344)( 94,343)( 95,342)
( 96,341)( 97,340)( 98,339)( 99,338)(100,337)(101,336)(102,335)(103,334)
(104,333)(105,332)(106,331)(107,330)(108,329)(109,328)(110,327)(111,326)
(112,325)(113,324)(114,323)(115,322)(116,321)(117,378)(118,406)(119,405)
(120,404)(121,403)(122,402)(123,401)(124,400)(125,399)(126,398)(127,397)
(128,396)(129,395)(130,394)(131,393)(132,392)(133,391)(134,390)(135,389)
(136,388)(137,387)(138,386)(139,385)(140,384)(141,383)(142,382)(143,381)
(144,380)(145,379)(146,349)(147,377)(148,376)(149,375)(150,374)(151,373)
(152,372)(153,371)(154,370)(155,369)(156,368)(157,367)(158,366)(159,365)
(160,364)(161,363)(162,362)(163,361)(164,360)(165,359)(166,358)(167,357)
(168,356)(169,355)(170,354)(171,353)(172,352)(173,351)(174,350)(175,436)
(176,464)(177,463)(178,462)(179,461)(180,460)(181,459)(182,458)(183,457)
(184,456)(185,455)(186,454)(187,453)(188,452)(189,451)(190,450)(191,449)
(192,448)(193,447)(194,446)(195,445)(196,444)(197,443)(198,442)(199,441)
(200,440)(201,439)(202,438)(203,437)(204,407)(205,435)(206,434)(207,433)
(208,432)(209,431)(210,430)(211,429)(212,428)(213,427)(214,426)(215,425)
(216,424)(217,423)(218,422)(219,421)(220,420)(221,419)(222,418)(223,417)
(224,416)(225,415)(226,414)(227,413)(228,412)(229,411)(230,410)(231,409)
(232,408)(465,697)(466,725)(467,724)(468,723)(469,722)(470,721)(471,720)
(472,719)(473,718)(474,717)(475,716)(476,715)(477,714)(478,713)(479,712)
(480,711)(481,710)(482,709)(483,708)(484,707)(485,706)(486,705)(487,704)
(488,703)(489,702)(490,701)(491,700)(492,699)(493,698)(494,726)(495,754)
(496,753)(497,752)(498,751)(499,750)(500,749)(501,748)(502,747)(503,746)
(504,745)(505,744)(506,743)(507,742)(508,741)(509,740)(510,739)(511,738)
(512,737)(513,736)(514,735)(515,734)(516,733)(517,732)(518,731)(519,730)
(520,729)(521,728)(522,727)(523,755)(524,783)(525,782)(526,781)(527,780)
(528,779)(529,778)(530,777)(531,776)(532,775)(533,774)(534,773)(535,772)
(536,771)(537,770)(538,769)(539,768)(540,767)(541,766)(542,765)(543,764)
(544,763)(545,762)(546,761)(547,760)(548,759)(549,758)(550,757)(551,756)
(552,784)(553,812)(554,811)(555,810)(556,809)(557,808)(558,807)(559,806)
(560,805)(561,804)(562,803)(563,802)(564,801)(565,800)(566,799)(567,798)
(568,797)(569,796)(570,795)(571,794)(572,793)(573,792)(574,791)(575,790)
(576,789)(577,788)(578,787)(579,786)(580,785)(581,842)(582,870)(583,869)
(584,868)(585,867)(586,866)(587,865)(588,864)(589,863)(590,862)(591,861)
(592,860)(593,859)(594,858)(595,857)(596,856)(597,855)(598,854)(599,853)
(600,852)(601,851)(602,850)(603,849)(604,848)(605,847)(606,846)(607,845)
(608,844)(609,843)(610,813)(611,841)(612,840)(613,839)(614,838)(615,837)
(616,836)(617,835)(618,834)(619,833)(620,832)(621,831)(622,830)(623,829)
(624,828)(625,827)(626,826)(627,825)(628,824)(629,823)(630,822)(631,821)
(632,820)(633,819)(634,818)(635,817)(636,816)(637,815)(638,814)(639,900)
(640,928)(641,927)(642,926)(643,925)(644,924)(645,923)(646,922)(647,921)
(648,920)(649,919)(650,918)(651,917)(652,916)(653,915)(654,914)(655,913)
(656,912)(657,911)(658,910)(659,909)(660,908)(661,907)(662,906)(663,905)
(664,904)(665,903)(666,902)(667,901)(668,871)(669,899)(670,898)(671,897)
(672,896)(673,895)(674,894)(675,893)(676,892)(677,891)(678,890)(679,889)
(680,888)(681,887)(682,886)(683,885)(684,884)(685,883)(686,882)(687,881)
(688,880)(689,879)(690,878)(691,877)(692,876)(693,875)(694,874)(695,873)
(696,872);
s1 := Sym(928)!( 1, 2)( 3, 29)( 4, 28)( 5, 27)( 6, 26)( 7, 25)( 8, 24)
( 9, 23)( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)
( 32, 58)( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)
( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)
( 63, 85)( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)
( 71, 77)( 72, 76)( 73, 75)( 88, 89)( 90,116)( 91,115)( 92,114)( 93,113)
( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)
(102,104)(117,147)(118,146)(119,174)(120,173)(121,172)(122,171)(123,170)
(124,169)(125,168)(126,167)(127,166)(128,165)(129,164)(130,163)(131,162)
(132,161)(133,160)(134,159)(135,158)(136,157)(137,156)(138,155)(139,154)
(140,153)(141,152)(142,151)(143,150)(144,149)(145,148)(175,205)(176,204)
(177,232)(178,231)(179,230)(180,229)(181,228)(182,227)(183,226)(184,225)
(185,224)(186,223)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)
(193,216)(194,215)(195,214)(196,213)(197,212)(198,211)(199,210)(200,209)
(201,208)(202,207)(203,206)(233,292)(234,291)(235,319)(236,318)(237,317)
(238,316)(239,315)(240,314)(241,313)(242,312)(243,311)(244,310)(245,309)
(246,308)(247,307)(248,306)(249,305)(250,304)(251,303)(252,302)(253,301)
(254,300)(255,299)(256,298)(257,297)(258,296)(259,295)(260,294)(261,293)
(262,321)(263,320)(264,348)(265,347)(266,346)(267,345)(268,344)(269,343)
(270,342)(271,341)(272,340)(273,339)(274,338)(275,337)(276,336)(277,335)
(278,334)(279,333)(280,332)(281,331)(282,330)(283,329)(284,328)(285,327)
(286,326)(287,325)(288,324)(289,323)(290,322)(349,437)(350,436)(351,464)
(352,463)(353,462)(354,461)(355,460)(356,459)(357,458)(358,457)(359,456)
(360,455)(361,454)(362,453)(363,452)(364,451)(365,450)(366,449)(367,448)
(368,447)(369,446)(370,445)(371,444)(372,443)(373,442)(374,441)(375,440)
(376,439)(377,438)(378,408)(379,407)(380,435)(381,434)(382,433)(383,432)
(384,431)(385,430)(386,429)(387,428)(388,427)(389,426)(390,425)(391,424)
(392,423)(393,422)(394,421)(395,420)(396,419)(397,418)(398,417)(399,416)
(400,415)(401,414)(402,413)(403,412)(404,411)(405,410)(406,409)(465,582)
(466,581)(467,609)(468,608)(469,607)(470,606)(471,605)(472,604)(473,603)
(474,602)(475,601)(476,600)(477,599)(478,598)(479,597)(480,596)(481,595)
(482,594)(483,593)(484,592)(485,591)(486,590)(487,589)(488,588)(489,587)
(490,586)(491,585)(492,584)(493,583)(494,611)(495,610)(496,638)(497,637)
(498,636)(499,635)(500,634)(501,633)(502,632)(503,631)(504,630)(505,629)
(506,628)(507,627)(508,626)(509,625)(510,624)(511,623)(512,622)(513,621)
(514,620)(515,619)(516,618)(517,617)(518,616)(519,615)(520,614)(521,613)
(522,612)(523,640)(524,639)(525,667)(526,666)(527,665)(528,664)(529,663)
(530,662)(531,661)(532,660)(533,659)(534,658)(535,657)(536,656)(537,655)
(538,654)(539,653)(540,652)(541,651)(542,650)(543,649)(544,648)(545,647)
(546,646)(547,645)(548,644)(549,643)(550,642)(551,641)(552,669)(553,668)
(554,696)(555,695)(556,694)(557,693)(558,692)(559,691)(560,690)(561,689)
(562,688)(563,687)(564,686)(565,685)(566,684)(567,683)(568,682)(569,681)
(570,680)(571,679)(572,678)(573,677)(574,676)(575,675)(576,674)(577,673)
(578,672)(579,671)(580,670)(697,901)(698,900)(699,928)(700,927)(701,926)
(702,925)(703,924)(704,923)(705,922)(706,921)(707,920)(708,919)(709,918)
(710,917)(711,916)(712,915)(713,914)(714,913)(715,912)(716,911)(717,910)
(718,909)(719,908)(720,907)(721,906)(722,905)(723,904)(724,903)(725,902)
(726,872)(727,871)(728,899)(729,898)(730,897)(731,896)(732,895)(733,894)
(734,893)(735,892)(736,891)(737,890)(738,889)(739,888)(740,887)(741,886)
(742,885)(743,884)(744,883)(745,882)(746,881)(747,880)(748,879)(749,878)
(750,877)(751,876)(752,875)(753,874)(754,873)(755,843)(756,842)(757,870)
(758,869)(759,868)(760,867)(761,866)(762,865)(763,864)(764,863)(765,862)
(766,861)(767,860)(768,859)(769,858)(770,857)(771,856)(772,855)(773,854)
(774,853)(775,852)(776,851)(777,850)(778,849)(779,848)(780,847)(781,846)
(782,845)(783,844)(784,814)(785,813)(786,841)(787,840)(788,839)(789,838)
(790,837)(791,836)(792,835)(793,834)(794,833)(795,832)(796,831)(797,830)
(798,829)(799,828)(800,827)(801,826)(802,825)(803,824)(804,823)(805,822)
(806,821)(807,820)(808,819)(809,818)(810,817)(811,816)(812,815);
s2 := Sym(928)!( 1,465)( 2,466)( 3,467)( 4,468)( 5,469)( 6,470)( 7,471)
( 8,472)( 9,473)( 10,474)( 11,475)( 12,476)( 13,477)( 14,478)( 15,479)
( 16,480)( 17,481)( 18,482)( 19,483)( 20,484)( 21,485)( 22,486)( 23,487)
( 24,488)( 25,489)( 26,490)( 27,491)( 28,492)( 29,493)( 30,494)( 31,495)
( 32,496)( 33,497)( 34,498)( 35,499)( 36,500)( 37,501)( 38,502)( 39,503)
( 40,504)( 41,505)( 42,506)( 43,507)( 44,508)( 45,509)( 46,510)( 47,511)
( 48,512)( 49,513)( 50,514)( 51,515)( 52,516)( 53,517)( 54,518)( 55,519)
( 56,520)( 57,521)( 58,522)( 59,552)( 60,553)( 61,554)( 62,555)( 63,556)
( 64,557)( 65,558)( 66,559)( 67,560)( 68,561)( 69,562)( 70,563)( 71,564)
( 72,565)( 73,566)( 74,567)( 75,568)( 76,569)( 77,570)( 78,571)( 79,572)
( 80,573)( 81,574)( 82,575)( 83,576)( 84,577)( 85,578)( 86,579)( 87,580)
( 88,523)( 89,524)( 90,525)( 91,526)( 92,527)( 93,528)( 94,529)( 95,530)
( 96,531)( 97,532)( 98,533)( 99,534)(100,535)(101,536)(102,537)(103,538)
(104,539)(105,540)(106,541)(107,542)(108,543)(109,544)(110,545)(111,546)
(112,547)(113,548)(114,549)(115,550)(116,551)(117,610)(118,611)(119,612)
(120,613)(121,614)(122,615)(123,616)(124,617)(125,618)(126,619)(127,620)
(128,621)(129,622)(130,623)(131,624)(132,625)(133,626)(134,627)(135,628)
(136,629)(137,630)(138,631)(139,632)(140,633)(141,634)(142,635)(143,636)
(144,637)(145,638)(146,581)(147,582)(148,583)(149,584)(150,585)(151,586)
(152,587)(153,588)(154,589)(155,590)(156,591)(157,592)(158,593)(159,594)
(160,595)(161,596)(162,597)(163,598)(164,599)(165,600)(166,601)(167,602)
(168,603)(169,604)(170,605)(171,606)(172,607)(173,608)(174,609)(175,639)
(176,640)(177,641)(178,642)(179,643)(180,644)(181,645)(182,646)(183,647)
(184,648)(185,649)(186,650)(187,651)(188,652)(189,653)(190,654)(191,655)
(192,656)(193,657)(194,658)(195,659)(196,660)(197,661)(198,662)(199,663)
(200,664)(201,665)(202,666)(203,667)(204,668)(205,669)(206,670)(207,671)
(208,672)(209,673)(210,674)(211,675)(212,676)(213,677)(214,678)(215,679)
(216,680)(217,681)(218,682)(219,683)(220,684)(221,685)(222,686)(223,687)
(224,688)(225,689)(226,690)(227,691)(228,692)(229,693)(230,694)(231,695)
(232,696)(233,697)(234,698)(235,699)(236,700)(237,701)(238,702)(239,703)
(240,704)(241,705)(242,706)(243,707)(244,708)(245,709)(246,710)(247,711)
(248,712)(249,713)(250,714)(251,715)(252,716)(253,717)(254,718)(255,719)
(256,720)(257,721)(258,722)(259,723)(260,724)(261,725)(262,726)(263,727)
(264,728)(265,729)(266,730)(267,731)(268,732)(269,733)(270,734)(271,735)
(272,736)(273,737)(274,738)(275,739)(276,740)(277,741)(278,742)(279,743)
(280,744)(281,745)(282,746)(283,747)(284,748)(285,749)(286,750)(287,751)
(288,752)(289,753)(290,754)(291,784)(292,785)(293,786)(294,787)(295,788)
(296,789)(297,790)(298,791)(299,792)(300,793)(301,794)(302,795)(303,796)
(304,797)(305,798)(306,799)(307,800)(308,801)(309,802)(310,803)(311,804)
(312,805)(313,806)(314,807)(315,808)(316,809)(317,810)(318,811)(319,812)
(320,755)(321,756)(322,757)(323,758)(324,759)(325,760)(326,761)(327,762)
(328,763)(329,764)(330,765)(331,766)(332,767)(333,768)(334,769)(335,770)
(336,771)(337,772)(338,773)(339,774)(340,775)(341,776)(342,777)(343,778)
(344,779)(345,780)(346,781)(347,782)(348,783)(349,842)(350,843)(351,844)
(352,845)(353,846)(354,847)(355,848)(356,849)(357,850)(358,851)(359,852)
(360,853)(361,854)(362,855)(363,856)(364,857)(365,858)(366,859)(367,860)
(368,861)(369,862)(370,863)(371,864)(372,865)(373,866)(374,867)(375,868)
(376,869)(377,870)(378,813)(379,814)(380,815)(381,816)(382,817)(383,818)
(384,819)(385,820)(386,821)(387,822)(388,823)(389,824)(390,825)(391,826)
(392,827)(393,828)(394,829)(395,830)(396,831)(397,832)(398,833)(399,834)
(400,835)(401,836)(402,837)(403,838)(404,839)(405,840)(406,841)(407,871)
(408,872)(409,873)(410,874)(411,875)(412,876)(413,877)(414,878)(415,879)
(416,880)(417,881)(418,882)(419,883)(420,884)(421,885)(422,886)(423,887)
(424,888)(425,889)(426,890)(427,891)(428,892)(429,893)(430,894)(431,895)
(432,896)(433,897)(434,898)(435,899)(436,900)(437,901)(438,902)(439,903)
(440,904)(441,905)(442,906)(443,907)(444,908)(445,909)(446,910)(447,911)
(448,912)(449,913)(450,914)(451,915)(452,916)(453,917)(454,918)(455,919)
(456,920)(457,921)(458,922)(459,923)(460,924)(461,925)(462,926)(463,927)
(464,928);
poly := sub<Sym(928)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope